Best Known (159, 204, s)-Nets in Base 4
(159, 204, 1052)-Net over F4 — Constructive and digital
Digital (159, 204, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 51, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(159, 204, 3880)-Net over F4 — Digital
Digital (159, 204, 3880)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4204, 3880, F4, 45) (dual of [3880, 3676, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(4204, 4119, F4, 45) (dual of [4119, 3915, 46]-code), using
- construction X applied to Ce(44) ⊂ Ce(40) [i] based on
- linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(44) ⊂ Ce(40) [i] based on
- discarding factors / shortening the dual code based on linear OA(4204, 4119, F4, 45) (dual of [4119, 3915, 46]-code), using
(159, 204, 1084167)-Net in Base 4 — Upper bound on s
There is no (159, 204, 1084168)-net in base 4, because
- 1 times m-reduction [i] would yield (159, 203, 1084168)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 165 265815 531463 438521 706972 529801 309677 455545 361932 238403 642004 618308 267763 431378 389031 554190 569690 656155 413736 227940 381552 > 4203 [i]